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<p>In this paper, we establish that the general Hausdorff and packing measures can be represented as variation measures. As a practical demonstration, we present integral expressions for the density outcomes of these measures, expanding upon existing knowledge. Furthermore, we investigate the equivalence between the general Hausdorff and packing measures on cookie-cutter-like sets that adhere to the strong separation condition.</p>

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General fractal measures: fine variation and density results

  • 期刊论文

  • 发表日期：

    2025年5月31日

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  • Yongjun Zhang,
  • Rim Achour,
  • Haythem Zyoudi

摘要

In this paper, we establish that the general Hausdorff and packing measures can be represented as variation measures. As a practical demonstration, we present integral expressions for the density outcomes of these measures, expanding upon existing knowledge. Furthermore, we investigate the equivalence between the general Hausdorff and packing measures on cookie-cutter-like sets that adhere to the strong separation condition.